Quadratic Equations

What can the roots to a quadratic equation be called?

• zeros

• solutions

• x-intercepts

• none of the choices

What are the green dots called?

• axis of symmetry
• vertex
• parabola
• roots or x-intercepts

What are the x- intercepts?

• x= 0 and x= -4
• x= 0 and x= 4
• y= 0
• x= 2

Solve for the values of x:
(x + 2)(x - 3) = 0

• { 2, 3 }
• { -2, -3 }
• { 2, 3 }
• { -2, 3 }

In quadratic equation ax² + bx + c = 0, what is the quadratic term?

• ax²

• bx

• c

• 0

Answer explanation

Correct!

Remember that quadratic means having a degree of 2 so ax² is the quadratic term, bx is the linear term (having 1 degree), and c is the constant term (only a number)

In 2x² + 5x - 3 = 0, what is the linear term?

• 2x²

• 5x

• -3

• 0

Answer explanation

Correct!

2x² is the quadratic term which contains the exponent of 2,

5x is the linear term which contains the exponent of 1 which is automatically understood and not written in the expression,

-3 is the constant which is the number only.

What are the values for a, b, and c in the quadratic equation 3x² - 6x - 10 = 0?

• a = 3, b = 6, c = 10

• a = 3, b = -6, c = -10

• a = 3, b = -6, c = 10

• a = -3, b = 6, c = 10

Answer explanation

Correct!

Remember the standard form of quadratic equation ax² + bx + c = 0, a, b, and c are coefficients which represent values for instance in 3x² - 6x - 10 = 0,

a is positive 3, b is negative 6 since we have -6x meaning the linear term is negative and also the constant is negative which -3.

Is 2x(x - 3) = 15 a quadratic equation? If yes, then what is its standard form when written as ax² + bx + c = 0?

• 2x² - 6x - 15 = 0

• 2x² - 3x - 15 = 0

• 2x² - 6x = 15

• no, it's not a quadratic equation

Answer explanation

Correct!

2x(x - 3) = 15 is a quadratic equation because if we are going to write this in the standard form ax² + bx + c = 0, using distributive property, we can have 2x times x is 2x², 2x times -3 is -6x and to write this in standard form, we have to transpose or to change the location of the constant which is 15 to the left side of the equal sign. We have to apply addition property of equality or APE by adding -15 to both sides of the equation.

ax²+bx+c=0  is the standard form of a quadratic equation.

• True
• False

Determine the values of
a, b, and c for
the quadratic equation: 
4x² – 8x = 3

• a = 4, b = -8, c = 3
• a = 4, b =-8, c =-3
• a = 4, b = 8, c = 3
• a = 4, b = 8, c = -3